Many historical and universal facts and data support that East Sea is the more appropriate notation compared to Sea of Japan. Firstly, Sea of Japan is a remainder of the history between Japan and South Korea.
Japan ruled South Korea as a colony in the early 20th century.
Secondly, "East Sea" is a name used since a long time ago between Koreans.
Also, "East Sea" was used since a longer time than "Sea of Japan".
According to http://whyeastsea.prkorea.com/,
"The first record of "East Sea" was in The History of the Three Kingdoms and the Saga of King Dong-myeong and in the process of recording matters in around 59 B.C., "East Sea" appears.
Also, as time passes, "East Sea" is gaining support.